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Maximal function on Lorentz spaces with weights: new results, and open problems

Carlos Pérez
Institution: 
University of the Basque Country and BCAM - Spain
Location: 
Luigi Stasi Seminar Room, ICTP
Schedule: 
Wednesday, January 30, 2019 - 14:30
Abstract: 

The Hardy-Littlewood maximal function is a basic operator in Analysis. We propose to discuss some of the reasons why this operator plays a central role in the area. Then we will concentrate on some of the classical results making special emphasis in the behavior of this operator in the context of $L^p$ spaces with weights. Then we will explain some more recent results focusing in the context of Lorentz spaces which are very useful extensions of the Lebesgue spaces. We have obtained some new results for these spaces but we don't know if they are optimal. In the last part of the lecture we will discuss a very interesting variant of the Hardy-Littlewood maximal function which is more singular called the strong maximal function. We will discuss briefly some classical results and we will mention some recent results which, again, we don't know if the are optimal.

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